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Block #497,627

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/17/2014, 4:46:02 PM Β· Difficulty 10.7698 Β· 6,310,701 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
2fe0d1bd0e00d89d25b5742288e61c7e360de989ceb5e75fcf0b91ec69124783
View on Chainz β†—

Height

#497,627

Difficulty

10.769787

Transactions

2

Size

390 B

Version

2

Bits

0ac510be

Nonce

1,736,435,062

Timestamp

4/17/2014, 4:46:02 PM

Confirmations

6,310,701

Mined by

⛏️ P2SHAamoNDMf7jjSMiEcifdUwheqpJY9zE1ad6

Merkle Root

4d719f793f1a805cd561d752b7289e184727259b60b959373a86ee8df7fbca62
Transactions (2)
Coinbase617b82ce80bc8b…95f5b3c564d2d3
1 in β†’ 1 out8.6200 XPM109 B
AamoNDMf…Y9zE1ad6
b9a0d0fa025b94…6c984749f6fc85
1 in β†’ 1 out1.9900 XPM192 B
APvuAp7X…g5g4GpmV
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.539 Γ— 10⁹²(93-digit number)
65396302757088580539…20727960421316619109
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
6.539 Γ— 10⁹²(93-digit number)
65396302757088580539…20727960421316619109
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.307 Γ— 10⁹³(94-digit number)
13079260551417716107…41455920842633238219
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.615 Γ— 10⁹³(94-digit number)
26158521102835432215…82911841685266476439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.231 Γ— 10⁹³(94-digit number)
52317042205670864431…65823683370532952879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.046 Γ— 10⁹⁴(95-digit number)
10463408441134172886…31647366741065905759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.092 Γ— 10⁹⁴(95-digit number)
20926816882268345772…63294733482131811519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.185 Γ— 10⁹⁴(95-digit number)
41853633764536691545…26589466964263623039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.370 Γ— 10⁹⁴(95-digit number)
83707267529073383090…53178933928527246079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁡(96-digit number)
16741453505814676618…06357867857054492159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.348 Γ— 10⁹⁡(96-digit number)
33482907011629353236…12715735714108984319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,710,679 XPMΒ·at block #6,808,327 Β· updates every 60s
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